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Graph Theory for Identifying Connectivity Patterns in Human Brain Networks

Graph Theory for Identifying Connectivity Patterns in Human Brain Networks

Functional connectivity and causal connections across different neural units are two main categories for how fMRI data on brain connectivity patterns are categorized. Recently, computational techniques—especially those based on graph theory—have been crucial in helping us comprehend the structure of brain connections.

In an effort to understand the neural bases of human cognition and neurological illnesses, a team at the University of Florida conducted a systematic review of how brain features might arise through the interactions of different neural units in various cognitive and neurological applications utilizing fMRI. This was made possible by the development of graph theoretical analysis.

A central and enduring aim of research in the psychological and brain sciences is to elucidate the information-processing architecture of human intelligence. Does intelligence originate from a specific brain structure or instead reflect system-wide network mechanisms for flexible and efficient information processing?

As neuroscientists work to comprehend the entire information behind cognition, behavior, and perception, studies on modeling the human brain as a complex system have significantly increased. The anatomical, functional, and causal structure of the human brain can be better understood by looking at connection patterns in the brain. Functional and effective connection among the connectivity methods have recently become the subject of computational investigations.

The topological design of human brain networks, including small-worldness, modularity, and highly linked or centralized hubs, may be understood by graph-based network analysis. Some networks have the trait of small-worldness, where most nodes can be reached from every other node with a minimal number of steps even when most of them are not neighbors. This property indicates effective information segregation and integration in the human brain networks with minimal energy and wiring costs, making it ideally suited for the study of complex brain dynamics.

FIGURE 1. Taxonomy of existing methods for modeling functional and effective connectivity patterns using fMRI. Each of the identified methods can be represented in terms of a graph, where the nodes correspond to cortical or subcortical regions and the edges represent (directed or undirected) connections (Bullmore and Sporns, 2012); thereby all of them can be further examined with graph-theoretic measures.

FIGURE 2. A network can be designed as binary (A) or weighted (B) graphs, and can represent the direction of causal effects (C,D) among different regions.

FIGURE 3. Schematic representation of brain network construction and graph theoretical analysis using fMRI data. After processing (B) the raw fMRI data (A) and division of the brain into different parcels (C), several time courses are extracted from each region (D) so that they can create the correlation matrix (E). To reduce the complexity and enhance the visual understanding, the binary correlation matrix (F), and the corresponding functional brain network (G) are constructed, respectively. Eventually, by quantifying a set of topological measures, graph analysis is performed on the brain’s connectivity network (H).

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FIGURE 4. Summary of global graph measures. (A) Segregation measures (B) Integration measure include characteristic path length (C) A regular network (left) displays a high clustering coefficient and a long average path length, while a random network (right) displays a low clustering coefficient and a short average path length. A small-world network (middle) illustrates an intermediate balance between regular and random networks (i.e., they consist of many short-range links alongside a few long-range links), reflecting a high clustering coefficient and a short path length. (D) The assortativity index

FIGURE 5. Basic concept of network centralities. (A) Hubs (connector or provincial) refer to nodes with a high nodal centrality, which can be identified using different measures. (B) The degree centrality

The researchers provided in-depth information on graph theoretical applications in neuroscience as well as the study of connection patterns in the complex brain network. The study’s findings indicate that graph theory and its applications to cognitive neuroscience are highly effective at describing the behavior of complex brain systems.

Cognitive function, behavioral variety, experimental task, and neurological conditions including epilepsy, Alzheimer’s disease, multiple sclerosis, autism, and attention-deficit/hyperactivity disorder are all likely to have an impact on the brain network architecture. The topological patterns of brain networks may be identified using graph theory metrics such as node degree, clustering coefficient, average path length, hubs, centrality, modularity, robustness, and assortativity, which can serve as indicators of cognitive and behavioral performance.

Application of Graph Theory for Identifying Connectivity Patterns in Human Brain Networks: A Systematic Review, Farzad V. Farahani, Waldemar Karwowski, and Nichole R. Lighthall
Published: June 2019
DOI: 10.3389/fnins.2019.00585

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